Question: Find the distance between the points (-5, 6) and (-6, -6). {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {\llap{-}10} {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {\llap{-}2} {\llap{-}3} {\llap{-}4} {\llap{-}5} {\llap{-}6} {\llap{-}7} {\llap{-}8} {\llap{-}9} {\llap{-}10} (-5, 6) (-6, -6) $1$ $12$
Change in $x$ -5 (-6) Change in $y$ (-6) 12 The distance is the length of the hypotenuse of this right triangle. By the Pythagorean Theorem, that length is equal to: $\sqrt{1^2 + 12^2}$ $= \sqrt{145}$